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# From a certain number of people who attended an interview

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Director
Joined: 17 Dec 2012
Posts: 627
Location: India
From a certain number of people who attended an interview  [#permalink]

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Updated on: 24 Jul 2013, 22:58
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

39% (02:02) correct 61% (02:21) wrong based on 150 sessions

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From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?

A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

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Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach

Originally posted by SravnaTestPrep on 24 Jul 2013, 21:40.
Last edited by fameatop on 24 Jul 2013, 22:58, edited 3 times in total.
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Re: From a certain number of people who attended an interview  [#permalink]

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24 Jul 2013, 22:18
SravnaTestPrep wrote:
From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x?
A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

nCx = nC(x+2) -----(Eq1)

or in other words,
x + x + 2 = n
2x+2 = n -----(Eq2)
So logically x can take any value as long as it satisfies both the equations.

X N
2 6
4 10
6 14
8 18

For all the above mentioned values of X & N both of the equations are satisfied.
So, answer should be E & not C.

Sravan, can you kindly confirm the OA once again.
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Director
Joined: 17 Dec 2012
Posts: 627
Location: India
Re: From a certain number of people who attended an interview  [#permalink]

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24 Jul 2013, 22:33
fameatop wrote:
SravnaTestPrep wrote:
From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x?
A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

nCx = nC(x+2) -----(Eq1)

or in other words,
x + x + 2 = n
2x+2 = n -----(Eq2)
So logically x can take any value as long as it satisfies both the equations.

X N
2 6
4 10
6 14
8 18

For all the above mentioned values of X & N both of the equations are satisfied.
So, answer should be E & not C.

Sravan, can you kindly confirm the OA once again.

Yes you are right. I was about to edit the question. Kindly take a look at it now.
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Director
Joined: 17 Dec 2012
Posts: 627
Location: India
Re: From a certain number of people who attended an interview  [#permalink]

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24 Jul 2013, 23:11
fameatop,

I guess you have not seen the question after I edited it. Your comment needs to be removed as the OA is A and not E.
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Manager
Status: How easy it is?
Joined: 09 Nov 2012
Posts: 89
Location: India
Concentration: Operations, General Management
GMAT 1: 650 Q50 V27
GMAT 2: 710 Q49 V37
GPA: 3.5
WE: Operations (Other)
Re: From a certain number of people who attended an interview  [#permalink]

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07 Aug 2013, 23:54
SravnaTestPrep wrote:
From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?

A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

Can you please provide an explanation for the OA?
Director
Joined: 17 Dec 2012
Posts: 627
Location: India
Re: From a certain number of people who attended an interview  [#permalink]

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08 Aug 2013, 00:07
2
SravnaTestPrep wrote:
From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?

A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

Solution:

1. We are selecting from the same number of people when x as well as x+2 selections are made and the number of selections that can be made is the same. i.e., nCx = nC(x+2)
i.e., x + (x+2) =n or
n=2x+2

2. The other information we have is that at least 2 interviews were conducted per day and the interviews were completed in 4 days. That is n has to be at least 2*4 = 8.

3. Now plug in the values of x from the answer choices. If x=2, n=6. This is not possible because it is less than 8. Other values are possible because n>8 in all those cases.
_________________
Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Senior Manager
Joined: 10 Jul 2013
Posts: 312
Re: From a certain number of people who attended an interview  [#permalink]

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08 Aug 2013, 00:29
1
nitin6305 wrote:
SravnaTestPrep wrote:
From a certain number of people who attended an interview, x people were selected. If instead, x+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of x if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?

A. 2
B. 4
C. 6
D. 8
E. Cannot be determined

Can you please provide an explanation for the OA?

solution:
At least 2 interviews a day, so minimum 8 interviews in four days. Thus at least a total of 8 candidates should be there.

Let, total candidates = n
according to the question,
nCx = nC(x+2)
or, nCn-x = nCx+2 [nCr = nCn-r]
or, n-x = x+2
so, n = 2x+2

Remember total least number should be 8? So below 8 we can't expect anything.
Put x=2, then n=6 that is unacceptable.
so x is not equal to 2 . Answer: A
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Re: From a certain number of people who attended an interview  [#permalink]

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23 Aug 2017, 04:08
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Re: From a certain number of people who attended an interview   [#permalink] 23 Aug 2017, 04:08
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